She is going to solve this problem. By taking some surveys. As in, grab photo paper, gather up a list of lines to go visit, and then knock on some doors and ask some questions and create a book series that organizes all possible forms, all known forms, what known lines look like in the forms - that sort of thing.
She starts with blue groups, because blue groups have the most available forms - she's gotten all of the big lines (well, all of the big lines that gave her the time of day) and is on the smaller ones. The ones with only one or two people. Or, in some cases, none.
This particular one's easier than some others; she doesn't need to fly to another country. It's Esmaar. She flies to the address of one 'Avar,' no line name. Apparently he had one and had some kind of explosive spat about it and gave it up. Not that it's her business. He's just another person for her survey.
She knocks on his door.
She smiles, just a little. Then her smile falters. "You know people are going to hate you for it. If we ever manage it. You probably won't get any peace for a long, long time. Possibly ever. It sounds kind of exhausting."
"Yeah. We already know something about how hard the other one's going to be to solve; let's find out how this one compares."
Step one to finding out how that compares: make a dragon magic analysis that shows what the dragon magic is doing, instead of where it is. This will likely take some time.
They are! It will take longer than an afternoon, though. Is Mial amenable to having scheduled nerd days with Avet?
Progress is... slow. Dragon magic declines to be easily analyzed. Inventing a spell for 'tell us what the dragon magic is doing' is not happening anytime soon, and neither of them are inclined to bang their heads against the brick wall of needing one specific solution.
It's much more reasonable to work on a dragon magic analysis that will tell them which part of the magic is moving when a dragonish does something magic. For example: speaking Draconic to one another, and seeing which part of the magic wibbles. They have charts, now. They can't narrow down everything that way, but they can certainly make progress. Speaking Draconic, shapeshifting, and singing a dragonish's dragonsong are easy. Green color group's empathy is similarly easy. A dragonish declining or trying to have kids is... Less easy. On account of no one wanting to watch a dragonish declining or trying to have kids.
A dragonish breathing fire should be easy. But Avet's wizard buddy is a shren. And she is a dragon. She could possibly go ask his mother to do the analysis on her instead of having Mial do it. But that sort of problem-dodging solution is not one she wants. She looks pensively at the chart.
"...It occurs to me that my father is a dragon and my mother is a research wizard," he says. "If, um. If we wanted to ask her to gather data for the 'declining to have children' section of the chart."
"If it wouldn't be um, too awkward. Then yeah, that would be helpful." She pauses, looking at the chart. Okay, this is stupid. She takes a deep breath. C'mon Avet, you can do it, it's just a sentence. "And we can go take care of the firebreathing data in your yard, if you're. Um. Okay with it."
"Sure I am. Are you? It's not very likely that either of us will spontaneously lose a form in the middle of my yard, but accidents happen. And my mother is a research wizard. If you wanted to ask her to do the firebreathing analysis, I wouldn't hold it against you."
"It's not really a matter of if you'd hold it against me," she says. "It's - I am poking at my reasons for not being okay with it and they're flimsy and I don't think they're good enough to have command over my life. I trust you. Finnah's at work and even if she were here, I trust her reasonably well. I don't think a random shren is going to show up out of nowhere and turn out to be the correct flavor of cruel and spiteful. I don't think either of us will spontaneously lose a form. There is no legitimate reason to be afraid. I don't want to have a, a flinch reaction to something in my head that I don't actually agree with, and let it control my life. I don't want to be that kind of person. If I were legitimately afraid I wouldn't volunteer, and I'd possibly be kind of upset with you if you expected me to, but this is - the sort of thing I am inclined to conquer, not cower from. So it's not, actually, involved with you at all, you're an innocent bystander." Pause. "So uh, sorry, innocent bystander, I am still attacking the lizard parts of my head, it takes a while. It's kind of entrenched."
"Yep," she agrees. "Though, uh, if you'd like me to analyze your firebreathing we should do it someplace that is not, er, your yard. It's not officially a shren hazard location. Bottom of the world or something would be better, I think."
"Yeah, I in fact already have a place on the bottom of the world where I go to shift natural and breathe fire at things. Because sometimes my contempt for certain letters to the editor cannot be fully expressed any other way."
Out they go, to do that. And then when they're out there, Avet shifts to natural form and obligingly breathes fire up at the sky once the spell's been cast.
"So that's most of everything," she muses. "I might grab my flight form early for the sake of studying it now, it's not like I'm likely to change my mind on it, I haven't budged since I picked it."